Presently, the heat energy or BTU content of a combustible fluid is measured by physically burning precisely defined amounts of the fluid, such as natural gas, to determine the amount of energy produced from the combustion. Other methods measure the concentration of each whole combustible compound in the mixture, defining the energy content for each whole compound, and summing them to yield the heat energy content of the entire mixture.
The heat energy content of natural gas in a pipeline or flowline frequently fluctuates within an hour or less. Natural gas typically contains 60-80% methane, 5-9% ethane, 3-18% propane, and 2-14% higher alkane hydrocarbons. These molecules possess an assortment of CH.sub.4 (methane), CH.sub.3, CH.sub.2, and CH functional groups. Mercaptan odorants, also combustible, are added to provide a distinctive warning odor for reason of safety. Present methods of measurement require bypass flowlines or fluid extraction to provide samples of gas which are taken to a laboratory and burned. The temperature of the flame is then measured. It is difficult to measure the energy content of natural gas in a pipeline both continuously and accurately. Improper charges may result over the course of a day to the disadvantage of both the buyer and seller.
Infrared spectroscopy is one of several types of spectroscopy capable of identifying and quantifying the functional groups of a given compound or mixture as an intermediate step to identifying one or more whole molecules. Infrared radiation causes groups of atoms of organic compounds to vibrate about their covalent bonds. Because of the vibrations, the groups of atoms absorb a quantified amount of infrared energy in particular regions of the spectrum. Each absorptive region is typically specified in frequency units by its wavenumber, measured in reciprocal centimeters. Infrared spectroscopy presently uses many such regions over a spectrum as broad as 200 cm.sup.-1 to 4000 cm.sup.-1, since the vibrations result in a variety of stretching and bending of the covalent bonds at different frequencies. The frequency of a given stretching vibration is related to the masses of the bonded atoms and the relative stiffness of the bond.
These mass and bond factors are useful for identifying various hydrocarbons, containing only carbon and hydrogen atoms. A number of absorptive regions are typically examined during the molecule identification process. Carbon-carbon single bonds of alkanes normally give rise to weak absorption peaks that are of relatively little use in identifying compounds. Carbon-carbon double bonds of alkenes provide absorption peaks in the 1620-1680 cm.sup.-1 region and carbon-carbon triple bonds of alkynes give absorption peaks of approximately 2100-2260 cm.sup.-1. Carbon-hydrogen stretching vibrations exhibit absorption peaks in the 2800-3300 cm.sup.-1 region. C--H bonds involving sp-hybridized carbon atoms are stronger than sp.sup.2 which are in turn greater in strength than sp.sup.3 bonds. The stronger bonds create peaks at higher frequencies.
Infrared spectral information regarding hydrocarbons is therefore used primarily to determine the type of bond between carbon atoms having one or more attached hydrogens for the purpose of separating alkanes, alkenes and alkynes, or for identifying a particular whole hydrocarbon molecule. It is difficult, however, to accurately distinguish between similar hydrocarbons possessing several identical functional groups.
The amount of monochromatic radiation absorbed by a fluid containing a single species is expressed by the Beer-Lambert law EQU A=abc
where A is the absorbance, a the absorptivity, b the path length or thickness of the sample, and c is the concentration of the species. When the path length is constant, the equation may be written as EQU A=kc
where a and b are combined to give a single proportionality constant k. Presently the species, or component, whose concentration is to be quantified is a whole molecule.
The relationship of concentration to absorbance at a single analytical frequency can be depicted graphically as a linear function. However, inter- and intramolecular interactions induce deviations from the Beer-Lambert law. A non-zero intercept may be added to approximate non-linear values over a limited region of the curve, giving EQU A=k.sub.1 c+k.sub.0
where k.sub.1, the slope, is the combined proportionality constant and k.sub.0 is the non-zero intercept.
The polychromatic radiation used by spectrometers and the chemical interactions among several components in a mixture cause further deviations in the Beer-Lambert law. One derivation of this law utilizes the absorbances of each of n components at several analytical wavelengths to generate simultaneous equations: ##EQU1## These equations may be expressed in matrix form as ##EQU2##
After the K matrix is calculated by measuring the spectra of individual known components, the concentrations of unknown components can be determined from measured absorbances using EQU C=K.sup.-1 A
A great disadvantage of this method is that the calculation of the K matrix does not reflect the interactions among molecules. It is known that a mixture of standards provides a more accurate approach. The A and C matrices may be extended to include a column of A's and a column of C's, respectively, for each standard, where each standard contains a mixture of species: ##EQU3## The K matrix is identical to the set of simultaneous equations presented above. Here, m.gtoreq.n, that is, there must be at least as many standard mixtures as the number of components. Solving for K requires some manipulation: since A and C are not necessarily square matrices, both sides of the previous equation may be multiplied by the transpose of C: EQU AC.sup.t =KCC.sup.t
and then the inverse of the square matrix (CC.sup.t) to yield EQU K=AC.sup.t (CC.sup.t).sup.-1
representing the least-squares fit of K. However, difficulties arise when a non-zero intercept is added. See Brown, C. W.; Lynch, P. F.; Obremski, R. J.; and Lavery, D. S., "Matrix Representations and Criteria for Selecting Analytical Wavelengths for Multicomponent Spectroscopic Analysis", 54 Anal. Chem. 1472-1479 (1982).
As presented by Brown et al., id., a preferred method of solving for K reverses the Beer-Lambert law to express concentration as a function of absorbance where ##EQU4##
The P matrix relates C to A. An additional column may be added to the right-hand side of the P matrix to allow for a non-zero intercept, in which case a last row of 1's is added to the A matrix. P is calculated through the least-squares method, such that EQU P=CA.sup.t (AA.sup.t).sup.-1
The concentrations of unknowns may also be calculated by EQU C=PA
See also Brown, C. W., and Lavery, D. S., "Multicomponent Infrared Analysis Using P-Matrix Methods", 12 J. Testing and Eval. 86-90 (1984); Maris, M. A.; Brown, C. W., and Lavery, D. S., "Nonlinear Multicomponent Analysis by Infrared Spectrophotometry", 55 Anal. Chem. 1694-1703 (1983).
As is true for spectroscopy in general, it is still difficult to distinguish between similar molecular components using the P matrix method, particularly when the components have one or more functional groups in common. More fundamentally, the P matrix and spectroscopy are presently directed toward determining the concentration of one or more components, where each component is a species of whole molecule. Physical properties, such as heat energy, that are related to the quantity of certain ingredients in a fluid are viewed in terms of the concentrations of the molecular species. Each molecular species has a known physical characteristic, such as heat of combustion, which is multiplied by the concentration of that species to determine its contribution toward the physical property of the fluid. The physical characteristic of each species must be summed to quantify the total physical property of the fluid. Since there must be at least as many standards as species, and each standard is measured at each wavelength, the calibration process is elaborate and time consuming and the resulting calculations are cumbersome.